Hormone replacement therapy

Martha Hickey, Jane Elliott, Sonia Louise Daviso

The Lipkin Model in the su(M+1)-Algebra for Many-Fermion System and its Counterpart in the Schwinger Boson Representation

Following the Schwinger boson representation for the su(M+1)- and the su(N,1)-algebra presented by two of the present authors (J. da P. and M. Y.) and Kuriyama, a possible counterpart of the Lipkin model in the su(M+1)-algebra formulated in the fermion space is presented. The free vacuum, which plays a fundamental role in the conventional treatment of the Lipkin model, is generalized in a quite natural way, and further, the excited state generating operators such as the particle-hole pairs are also given in a natural scheme. As concrete examples, the cases of the su(2)-, su(3)- and the su(4)-algebra are discussed. Especially, the case of the su(4)-algebra is investigated in detail in relation to the nucleon pairing correlations and the high temperature superconductivity.Comment: 22 pages, 1 figure, using PTPTeX styl

Financial signal processing: a self calibrating model

Previous work on multifactor term structure models has proposed that the short rate process is a function of some unobserved diffusion process. We consider a model in which the short rate process is a function of a Markov chain which represents the 'state of the world'. This enables us to obtain explicit expressions for the prices of zero-coupon bonds and other securities. Discretizing our model allows the use of signal processing techniques from Hidden Markov Models. This means we can estimate not only the unobserved Markov chain but also the parameters of the model, so the model is self-calibrating. The estimation procedure is tested on a selection of U.S. Treasury bills and bonds.Bonds

Acoustic test of a model rotor and tail rotor: Results for the isolated rotors and combined configuration

Acoustic data from a model scale main rotor and tail rotor experiment in the NASA Langley 14 by 22 Foot Subsonic Tunnel are presented for the main rotor and trail rotor in isolation and for the two rotors operating together. Results for the isolated main rotor show the importance of the rotor flapping conditions on mid-frequency noise content. High levels of main rotor retreating side blade-vortex interaction noise are shown to radiate downstream of the model. The isolated tail rotor noise results show the dominance of harmonic noise in the thrusting direction. The occurrence of tail rotor broadband noise is seen by the broadening of the tail rotor harmonics and is attributed to fuselage wake turbulence. The combined main and tail rotor data are presented to show the dominance of each rotor's different noise sources at different directivity locations

Modelling cell motility and chemotaxis with evolving surface finite elements

We present a mathematical and a computational framework for the modelling of cell motility. The cell membrane is represented by an evolving surface, with the movement of the cell determined by the interaction of various forces that act normal to the surface. We consider external forces such as those that may arise owing to inhomogeneities in the medium and a pressure that constrains the enclosed volume, as well as internal forces that arise from the reaction of the cells' surface to stretching and bending. We also consider a protrusive force associated with a reaction-diffusion system (RDS) posed on the cell membrane, with cell polarization modelled by this surface RDS. The computational method is based on an evolving surface finite-element method. The general method can account for the large deformations that arise in cell motility and allows the simulation of cell migration in three dimensions. We illustrate applications of the proposed modelling framework and numerical method by reporting on numerical simulations of a model for eukaryotic chemotaxis and a model for the persistent movement of keratocytes in two and three space dimensions. Movies of the simulated cells can be obtained from http://homepages.warwick.ac.uk/maskae/CV_Warwick/Chemotaxis.html

The ordered K-theory of a full extension

Let A be a C*-algebra with real rank zero which has the stable weak cancellation property. Let I be an ideal of A such that I is stable and satisfies the corona factorization property. We prove that 0->I->A->A/I->0 is a full extension if and only if the extension is stenotic and K-lexicographic. As an immediate application, we extend the classification result for graph C*-algebras obtained by Tomforde and the first named author to the general non-unital case. In combination with recent results by Katsura, Tomforde, West and the first author, our result may also be used to give a purely K-theoretical description of when an essential extension of two simple and stable graph C*-algebras is again a graph C*-algebra.Comment: Version IV: No changes to the text. We only report that Theorem 4.9 is not correct as stated. See arXiv:1505.05951 for more details. Since Theorem 4.9 is an application to the main results of the paper, the main results of this paper are not affected by the error. Version III comments: Some typos and errors corrected. Some references adde

Bubbles and Filaments: Stirring a Cahn-Hilliard Fluid

The advective Cahn-Hilliard equation describes the competing processes of stirring and separation in a two-phase fluid. Intuition suggests that bubbles will form on a certain scale, and previous studies of Cahn-Hilliard dynamics seem to suggest the presence of one dominant length scale. However, the Cahn-Hilliard phase-separation mechanism contains a hyperdiffusion term and we show that, by stirring the mixture at a sufficiently large amplitude, we excite the diffusion and overwhelm the segregation to create a homogeneous liquid. At intermediate amplitudes we see regions of bubbles coexisting with regions of hyperdiffusive filaments. Thus, the problem possesses two dominant length scales, associated with the bubbles and filaments. For simplicity, we use use a chaotic flow that mimics turbulent stirring at large Prandtl number. We compare our results with the case of variable mobility, in which growth of bubble size is dominated by interfacial rather than bulk effects, and find qualitatively similar results.Comment: 20 pages, 27 figures. RevTeX